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We present a detailed overview of the cosmological surveys that we aim to carry out with Phase 1 of the Square Kilometre Array (SKA1) and the science that they will enable. We highlight three main surveys: a medium-deep continuum weak lensing and low-redshift spectroscopic HI galaxy survey over 5 000 deg2; a wide and deep continuum galaxy and HI intensity mapping (IM) survey over 20 000 deg2 from 
$z = 0.35$
to 3; and a deep, high-redshift HI IM survey over 100 deg2 from 
$z = 3$
to 6. Taken together, these surveys will achieve an array of important scientific goals: measuring the equation of state of dark energy out to 
$z \sim 3$
with percent-level precision measurements of the cosmic expansion rate; constraining possible deviations from General Relativity on cosmological scales by measuring the growth rate of structure through multiple independent methods; mapping the structure of the Universe on the largest accessible scales, thus constraining fundamental properties such as isotropy, homogeneity, and non-Gaussianity; and measuring the HI density and bias out to 
$z = 6$
. These surveys will also provide highly complementary clustering and weak lensing measurements that have independent systematic uncertainties to those of optical and near-infrared (NIR) surveys like Euclid, LSST, and WFIRST leading to a multitude of synergies that can improve constraints significantly beyond what optical or radio surveys can achieve on their own. This document, the 2018 Red Book, provides reference technical specifications, cosmological parameter forecasts, and an overview of relevant systematic effects for the three key surveys and will be regularly updated by the Cosmology Science Working Group in the run up to start of operations and the Key Science Programme of SKA1.
Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a numerical model, we explore a broad range of three key dimensionless numbers: a thermal stratification parameter (the relative size of boundary temperature gradients to imposed vertical temperature gradients), 
$10^{-3}\leqslant S\leqslant 10^{4}$, a buoyancy parameter (the strength of applied boundary heat-flux anomalies), 
$10^{-2}\leqslant B\leqslant 10^{6}$, and the Ekman number (ratio of viscous to Coriolis forces), 
$10^{-6}\leqslant E\leqslant 10^{-4}$. We find both steady and time-dependent solutions and delineate the regime boundaries. We focus on steady-state solutions, for which a clear transition is found between a low 
$S$ regime, in which buoyancy dominates the dynamics, and a high 
$S$ regime, in which stratification dominates. For the low-
$S$ regime, we find that the characteristic flow speed scales as 
$B^{2/3}$, whereas for high-
$S$, the radial and horizontal velocities scale respectively as 
$u_{r}\sim S^{-1}$, 
$u_{h}\sim S^{-3/4}B^{1/4}$ and are confined within a thin layer of depth 
$(SB)^{-1/4}$ at the outer edge of the domain. For the Earth, if lower mantle heterogeneous structure is due principally to chemical anomalies, we estimate that the core is in the high-
$S$ regime and steady flows arising from strong outer boundary thermal anomalies cannot penetrate the stable layer. However, if the mantle heterogeneities are due to thermal anomalies and the heat-flux variation is large, the core will be in a low-
$S$ regime in which the stable layer is likely penetrated by boundary-driven flows.
